First-Order Rewritability of Frontier-Guarded Ontology-Mediated Queries

TL;DR

This paper investigates the conditions under which ontology-mediated queries with guarded rules can be rewritten as first-order queries, providing automata-based methods and complexity results.

Contribution

It introduces two automata-based approaches for FO-rewritability of guarded OMQs and establishes 2ExpTime-completeness of the problem.

Findings

Automata-based methods for FO-rewritability

Semantic characterizations of FO-rewritability

Complexity result: 2ExpTime-complete

Abstract

We focus on ontology-mediated queries (OMQs) based on (frontier-)guarded existential rules and (unions of) conjunctive queries, and we investigate the problem of FO-rewritability, i.e., whether an OMQ can be rewritten as a first-order query. We adopt two different approaches. The first approach employs standard two-way alternating parity tree automata. Although it does not lead to a tight complexity bound, it provides a transparent solution based on widely known tools. The second approach relies on a sophisticated automata model, known as cost automata. This allows us to show that our problem is 2ExpTime-complete. In both approaches, we provide semantic characterizations of FO-rewritability that are of independent interest.